# Groups and Constraints: Symmetry Breaking during Search

@inproceedings{Gent2002GroupsAC, title={Groups and Constraints: Symmetry Breaking during Search}, author={Ian P. Gent and Warwick Harvey and Tom Kelsey}, booktitle={CP}, year={2002} }

We present an interface between the ECLiPSe constraint logic programming system and the GAP computational abstract algebra system. The interface provides a method for efficiently dealing with large numbers of symmetries of constraint satisfaction problems for minimal programming effort. We also report an implementation of SBDS using the GAP-ECLiPSe interface which is capable of handling many more symmetries than previous implementations and provides improved search performance for symmetric…

## 109 Citations

### Tractable Symmetry Breaking Using Restricted Search Trees

- Computer ScienceECAI
- 2004

A new conceptual abstraction in symmetry breaking - the GE-tree is presented, and a polynomial-time algorithm for this construction in the case of CSPs with arbitrary value symmetries is given.

### Comparison of Symmetry Breaking Methods

- Computer ScienceCP
- 2003

Constraint satisfaction problems (CSPs) are often highly symmetric, so constraint programmers use symmetry breaking methods to exclude all but one in each equivalence class of solutions.

### New Developments in Symmetry Breaking in Search Using Computational Group Theory

- Computer ScienceAISC
- 2004

This paper analyzes the structure of symmetry groups of constraint satisfaction problems, and implements several combinations of GE-trees and the classical SBDD method for breaking all symmetries.

### Constraint Symmetry and Solution Symmetry

- Computer ScienceAAAI
- 2006

This work discusses how solution symmetry and constraint symmetry are related and shows that some CSP instances have many more solution symmetries than constraint symmetry.

### Symmetry Breaking in Numeric Constraint Problems

- Computer ScienceCP
- 2011

It is shown that, for the variable symmetries among those proposed, the proposed inequalities are but a specific case of a relaxation of the well-known LEX constraints extensively used for discrete CSPs.

### Lightweight dynamic symmetry breaking

- Computer ScienceConstraints
- 2013

Lightweight Dynamic Symmetry Breaking is presented, an automatic symmetry breaking method that is efficient enough to be used as a default, since it never yields a major slowdown while often giving major performance improvements.

### Partial symmetry breaking by local search in the group

- Computer ScienceConstraints
- 2012

A new method called Symmetry Breaking by Nonstationary Optimisation is described, which interleaves local search in the symmetry group with backtrack search on the constraint problem, which can be tuned to break each symmetry with an arbitrarily high probability with high runtime overhead.

### Symmetry Breaking Revisited

- Computer ScienceConstraints
- 2004

This paper presents a new method based on the symmetries of decisions taken from the root of the search tree that is theoretically more efficient as the size of each no-good is smaller and can be seen as an improvement of the SBDD method.

### Breaking Conditional Symmetry in Automated Constraint Modelling with CONJURE

- Computer ScienceECAI
- 2014

This work presents a systematic method by which the automated constraint modelling tool CONJURE can break conditional symmetry as it enters a model during refinement, and results in the automatic and complete removal of model symmetry for the entire problem class represented by the input specification.

### NuSBDS: An Easy to Use Symmetry Breaking System

- Computer ScienceCP
- 2003

The GHK-SBDS method of breaking symmetry requires the user to supply a generator set of a group representing the symmetries of the CSP.

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